A simple approximation of the Weibull renewal function

This paper proposes a simple approximation for the renewal function of the Weibull distribution with an increasing failure rate (i.e., the shape parameter being larger than one). It is developed for using in optimization of preventive maintenance policies. The approximation is a weighted geometer average of the cumulative distribution and hazard functions with the weight being a function of the shape parameter. The approximation is accurate for t up to a certain value of larger than the scale parameter.